It seems to me we get salvation mixed-up with living our lives in obedience to God. Obeying God is good, obeying His laws is good, and those who choose to live their lives without obedience have left themselves a serious up-hill climb to find God's outstretched arms. On the other hand, our redemption and salvation from this flesh life is totally dependent on God's grace and mercy.
I like this, and I'd say that's a fair commentary to truth. It also addresses well the accusation that there might not be a reason to care about sin in ones life. Clearly there is.
If man's obedience has no part in his salvation then how does God decide to whom He will extend grace and mercy and who He will withhold His grace and mercy from?
Please keep in mind that the gospel does not describe an ongoing salvation for say, as much as it describes growth from salvation. This is a big part of the debate. But for the sake of this thread, and to answer your question (whatchman333 may want to answer it his own way) we need to start with what's being said of salvation; that it is a one time event in ones life. At least the awareness and revelation to the one saved is. And so your question, a very good one, is how does God decide who will be saved if they can't effect by merit or works, or some condition they meet to be saved.
The answer is longer than the question, but the short of it is disturbing to most. However here it is.
By His own pleasure, will and desire to do so not for that man, but for His glory to all men.
Many find this offensive, but that's really all God has said, or even needs to say to us, because while this thing called Christianity as a religion may be for us, salvation is ultimately NOT ABOUT YOU. (when I say YOU I'm being general to all) It's about God.
To those offended by this some will simply ignore the whole idea of God and salvation, finding other religions that focus on them or no religion at all, or they will choose their own understanding to fit themselves. none of that means they are, or aren't, or won't be saved, but the three main arguments out there to answer your question of how God chooses beyond what he has already said are these.
1. The salvation of individuals is ultimately the result of their choice rather than divine appointment (alone). (We often label this as the Armenian view after Arminius, but it fits with the RCC as well.
2. Election is based upon God foreseeing the faith of certain individuals rather than only being in accordance with His pleasure and merciful will. (This is a skewed Protestant view that is not biblical in any way)
3. Election is conditional, based upon the acceptance of Jesus Christ and not the determination of God, even though God's grace is certainly involved in this process. (This is more in line with the RCC)
There are other points people, make and have made just on this thread. God is arbitrary, or God is unfair, or salvation is a crap shoot based on luck, but none of these fit Gods reasoning either, because God has clearly said that anyone can be saved. He's also said not everyone is, or will be, and he has clearly said all are born into sin and doomed to condemnation, but that he will have mercy on whom he bloody well chooses.
Here are four points about what we do know from the character of God about Gods choosing.
1. Election is grounded in God's moral character (i.e., goodness, compassion, empathy, integrity, non-duplicity, non-favoritism, justice, etc.)
2. God does have "causes and reasons" for His choices, though these are "internal" to God (i.e., not found in the creature). We know He is good and therefore can trust that He would make a better choice than we would.
3. He 'does NOTHING without reason' --- He 'does NOTHING rashly’. He has simply not revealed these reasons and causes to us--although they certainly exist. Since they haven’t been revealed, we cannot try to figure them out but since we know the trustworthiness of God we can rejoice in His wisdom. God does not 'lack just reasons’ for His actions. These 'just reasons' are merely hidden from us.
4. Salvation is not conditioned upon anything that God sees in us that makes us worthy of His choosing us. NONE of His decrees were done except justly and wisely".
It's not a matter of How God chooses, because it's not up to us. But it is evident whom God chooses. It is evident to that person and it is evident in some way to others. Anyone can be saved. Anyone. Seek and you will find. ask and it will be given.